Automata theory based on complete residuated lattice-valued logic: A categorical approach

Fuzzy Sets and Systems

Volumn 160, Issue 16, 2009, Pages 2416-2428

  Xing, Hongyan ^a   Qiu, Daowen ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Automata; Category; Non classical logic

Indexed keywords

AUTOMATA; CATEGORY; FINAL STATE; NON-CLASSICAL LOGIC; NONDETERMINISTIC AUTOMATA; RESIDUATED LATTICES; TECHNICAL CONTRIBUTION;

FINITE AUTOMATA; ROBOTS; SET THEORY;

TRANSLATION (LANGUAGES);

EID: 67349144636     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2009.01.007     Document Type: Article

References (39)

1. Arbib M.A., and Manes E.G. Machines in a category: an expository introduction. SIAM Rev. 16 (1974) 163-192
2. Arbib M.A., and Manes E.G. Basic concepts of category theory applicable to computation and control. In: Manes E.G. (Ed). Category Theory Applied to Computation and Control, Proc. First Internat. Symp. AMherst MA, 1974, Lecture Notes in Computer Science Vol. 25 (1975), Springer, Berlin 2-41
3. Arbib M.A., and Manes E.G. Fuzzy machines in a category. Bull. Anstral. Math. Soc. 13 (1975) 169-210
4. Arbib M.A., and Manes E.G. A categorist's view of automata and systems. In: Manes E.G. (Ed). Category Theory Applied to Computation and Control, Proc. First Internat. Symp. AMherst MA, 1974, Lecture Notes in Computer Science Vol. 25 (1975), Springer, Berlin 62-78
5. Barr M., and Wells C. Category Theory for Computing Science. second ed. (1996), Prentice-Hall International (UK) Limited, Englewood Cliffs, NJ
6. Dilworth R.P. Abstract residuation over lattices. Bull. Amer. Math. Soc. 44 (1938) 262-268
7. Dilworth R.P. Residuated lattices. Trans. Amer. Math. Soc. 45 (1939) 335-354
8. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic, New York
9. H. Ehrig, Kategorien und Automaton, Berlin, New York, 1972.
10. Eilenberg S. Automata, Languages and Machines Vol. A (1974), Academic Press, New York
11. Esteva F., Godo L., and Garcia-Cerdaña A. On the hierarchy of t-norm based residuated fuzzy logics. In: Orlowska E., and Fitting M. (Eds). Beyond Two: Theory and Applications of Multiple-valued Logic (2003), Physica-Verlag, Heidelberg 251-272
12. Girard J.-Y. Linear logic. Theoret. Comput. Sci. 50 (1987) 1-102
13. Goguen J.A. L-fuzzy sets. J. Math. Anal. Appl. 18 (1967) 145-174
14. Hájek P. Mathematics of Fuzzy Logic (1998), Kluwer Academic Publishers, Dordrecht
15. Höhle U. Commutative, residuated monoids. In: Höhle U., and Klement E.P. (Eds). Non-classical Logics and their Applications to Fuzzy Subsets (1995), Kluwer Academic Publishers, Dordrecht 53-106
16. A. Iorgulescu, Classes of BCK algebras-Part I, Preprint Series of the Institute of Mathematics of the Romanian Academy, Preprint No. 1, 2004, pp. 1-33.
17. T. Kowalski, H. Ono, Residuated Lattices: An Algebraic Glimpse at Logics Without Contraction, Monograph, 2001
18. Li Y.M. A categorical approach to lattice-valued fuzzy automata. Fuzzy Sets and Systems 156 (2006) 855-864
19. Malik D.S., and Mordeson J.N. Fuzzy Discrete Structures (2000), Physica-Verlag, Heidelberg, New York
20. Manes E. Algebraic Theories (1976), Springer, Berlin
21. Močkoř J. A category of fuzzy automata. Internat. J. General Systems 20 (1991) 73-82
22. Močkoř J. Fuzzy and non-deterministic automata. Soft Comput. 3 (1999) 221-226
23. Močkoř J. Semigroup homomorphisms and fuzzy automata. Soft Comput. 6 (2002) 423-427
24. Mordeson J.N., and Malik D.S. Fuzzy Automata and Languages: Theory and Applications (2002), Chapman & Hall, CRC, Boca Raton, London
25. H. Ono, Logic without contraction rule and residuated lattices I, manuscript, 2003.
26. J. Pavelka, On fuzzy logic I,II,III, Z. Math Logik Grund. Math. 25 (1979) 45-52; 119-134; 447-464.
27. Qiu D.W. Automata theory based on complete residuated latticed-valued logic (I). Sci. China (Ser. F) 44 6 (2001) 419-429
28. Qiu D.W. Automata theory based on complete residuated latticed-valued logic (II). Sci. China (Ser. F) 45 6 (2002) 442-452
29. Qiu D.W. Supervisory control of fuzzy discrete event systems: a formal approach. IEEE Trans. Systems Man Cybernet. 35 1 (2005) 72-88
30. Qiu D.W. Pumping lemma in automata theory based on complete residuated lattice-valued logic: a note. Fuzzy Sets and Systems 157 (2006) 2128-2138
31. Qiu D.W. A note on Trilla's CHC models. Artif. Intell. 171 (2007) 239-254
32. Rescher N. Many-Valued Logic (1969), McGraw-Hill, New York
33. Starke P.H. Abstract Automata (1969), VEB Deutscher Verlag der wiss, Berlin
34. V. Trnková, Automata and categories, in: Lecture Notes in Computer Science, Vol. 32, Springer, Berlin, 1975, pp. 160-166.
35. V. Trnková, Relational automata in a category and their languages, in: Lecture Notes in Computer Science, Vol. 56, Springer, Berlin, 1977, pp. 340-355.
36. V. Trnková, L-fuzzy functional automata, in: Lecture Notes in Computer Science, Vol. 74, Springer, Berlin, 1979, pp. 463-473.
37. W. Wechler, V. Dimitrov, R-fuzzy automata, in: Information Processing 74, Proc. of IFIP Congress 74, Stockholm, Sweden, August 5-10, 1974, pp. 657-660.
38. Wechler W. The Concept of Fuzziness in Automata and Language Theory (1978), Akademie-Verlag, Berlin
39. Xing H.Y., Qiu D.W., Liu F.C., and Fan Z.J. Equivalence in automata theory based on complete residuated lattice-valued logic. Fuzzy Sets and Systems 158 (2007) 1407-1422